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Commissioning and operating turbomachinery often create surprises especially with respect to vibration. Often not all the conditions are known under which these highly-efficient turbomachines have to operate. This case study deals with a four-stage three-pinion integrally geared centrifugal compressor. It was designed for an air separation plant in Germany to produce nitrogen and oxygen for an adjacent steel works. The compressor was driven via a standard gear-tooth coupling with a 1500 mm (59 inch) spacer shaft by an induction motor with speed of 1490 rpm and power of 4000 Kw (5400 hp). During commissioning, high vibrations were observed at the pinion shafts, which sometimes exceeded the trip levels. The elevated shaft vibration levels occurred for only about 10 minutes. This pattern was repeated once or twice per hour. For the rest of the time, the compressor operated within all the API vibration limits. Detailed measurements of shaft vibrations, of transient coupling torques (with strain gauges), and of transient electric power are presented as well as calculations of the torsional vibrations of the shaft train using the electric noise of the electric power supply as excitation source. The measure selected to reduce the shaft torques is described by means of which had been possible to reduce the radial shaft vibrations to acceptable levels.